# Journal of Mathematical Extension Volume:13 Issue: 4, Autumn 2019

• تاریخ انتشار: 1399/09/21
• تعداد عناوین: 12
|

The decisions on facility location are not only important in the industrial sector, such as determining the location of construction of factories and power plants, the deployment of equipment and departments in an industrial unit, the establishment of offices in cities, product distribution centers, etc., but also in the public and service sector, such as the location of police stations, emergency services, buses, restaurants, banks, health and medical sector, and so on. Since making better models can help more in achieving the desired goals, this paper examines and develops one of the important issues in ‘facility location-allocation’ called Capacitated P-Median Problem (CPMP). In this paper, by developing the CPMP mathematical planning model, we try to model the problem in a way that the service to customers according to the service level is effective in the optimum solution, and to some extent, brings CPMP closer to actual circumstances. Adding the service level will convert CPMP from a deterministic state to a stochastic model in which demands can have any distribution function. If the customer demand follows the normal distribution function, this stochastic model can be converted to a Mixed Integer Nonlinear Programming. This obtained model is used in a real case study, to develop tanks of an oil refinery so that the costs are minimized and the customer demand is met at an acceptable level. Also, comparing the new model with traditional CPMP Model through solving the real case study shows the power of the proposed model.

Keywords: Facility location, Capacitated P-Median Problem (CPMP), service level, normal distribution
• Oğuzhan Bahadır*, Siraj Uddin Pages 23-39

In this paper, we study slant submanifolds of Riemannian manifolds with Golden structure. A Riemannian manifold (M, ˜ g, ϕ ˜ ) is called a Golden Riemannian manifold if the (1, 1) tensor field ϕ on M˜ is a Golden structure, that is ϕ2 = ϕ + I and the metric ˜g is ϕ− compatible. First, we get some new results for submanifolds of a Riemannian manifold with Golden structure. Later we characterize slant submanifolds of a Riemannian manifold with Golden structure and provide some non-trivial examples of slant submanifolds of Golden Riemannian manifolds.

Keywords: Invariant submanifolds, anti-invariant, slantsubmanifolds, golden structure, riemannian manifolds
• Esra KIRMIZI ÇETİNALP*, Eylem GÜZEL KARPUZ, Recep ŞAHİN, Fırat ATEŞ Pages 41-55

In this paper, we obtain a complete rewriting system for monoid presentation of generalized extended Hecke group Hp,q, which is firstly defined in [8]. It gives an algorithm for getting normal form of elements and hence solving the word problem in this group. By using the normal form structure of elements of Hp,q, we also calculate growth series.

Keywords: Hecke groups, rewriting systems, normalform, growth series
• Arezoo Salimi, shervin sahebi*, Mansoureh Deldar Pages 57-68

Let R be a ring and M be a monoid. We introduce the notion of J-M-McCoy rings, as a generalization of J-McCoy and weak MMcCoy rings, and investigate their properties. It is proved that for u.p.- monoids M and N if R J(R) is reversible, then R is J-M ×N-McCoy. Also, it is shown that a ring R is J-M-McCoy if and only if R[[x]] is JM-McCoy if and only if Tn(R) is J-M-McCoy, while the J-M-McCoy property is not Morita invariant.

Keywords: McCoy rings, M-McCoy rings, J-McCoy rings, Weak M-McCoy rings, J-M-McCoy rings, reversible rings, J-semisimple rings, Armendariz rings
• Hamid MEHRAVARAN, Mahnaz Khanehgir*, Reza Allahyari Pages 69-89

In this paper, we introduce the notion of dislocated Sb-metric space and describe some xed point theorems concerning F-contraction in the setup of such spaces. We provide some examplesto verify the eectiveness and applicability of our main results.

Keywords: Sb-metric space, xed point, F-contraction, F-weak contraction
• Jamal Rezaei Roshan*, Hemant Kumar Nashin Pages 91-116

We propose a new notion of contraction mappings for two class of functions involving measure of noncompactness in Banach space and derive some basic Darbo type fixed and coupled fixed point results. This work includes and extends the results of Falset and Latrach[ Falset, J. G., Latrach, K. : On Darbo-Sadovskii's fixed point theorems type for abstract measures of (weak) noncompactness, Bull. Belg. Math. Soc. Simon Stevin 22 (2015), 797-812.] The results are also correlated with the classical generalized Banach fixed point theorems. Also we show the applicability of obtained results to the Volterra integral equations in Banach algebras.

Keywords: Measures of noncompactness, Darbo’s fixedpoint theorem, coupled fixed point, integral equations
• Esra Yolacan* Pages 117-130

The purpose of this writing is to present strong convergence theorems of the modified three step iteration process for G-nonexpansive mappings in Banach spaces with a graph. The results presented in this study extend and improve a number of results in the literature.

Keywords: G-nonexpansive mappings, common fixed point, directed graph
• Mahmoud Hassani, YASER KHATIB*MARYAM Amyari Pages 131-142

Let U be a Hilbert A-module and L(U) the set of all adjointable A-linear maps on U. Let K = {Λx ∈ L(U, Vx) : x ∈ X } and L = {Γx ∈ L(U, Vx) : x ∈ X } be two continuous g-frames for U, K is said to be similar with L if there exists an invertible operator J ∈ L(U) such that Γx = ΛxJ, for all x ∈ X . In this paper, we define the concepts of closeness and nearness between two continuous g-frames. In particular, we show that K and L are near, if and only if they are similar.

Keywords: Hilbert C∗-modules, closeness bound, nearcontinuous g-frames, nearness
• Ishfaq Ahmad Malik*, Tanweer Jalal Pages 143-159

In this paper we first introduce N¯ q ∆− summable difference sequence spaces and prove some properties of these spaces. We then obtain the necessary and sufficient conditions for infinite matrix A to map these sequence spaces on the spaces c, c0 and ∞. Finally, the Hausdorff measure of noncompactness is used to obtain the necessary and sufficient conditions for the compactness of the linear operators defined on these spaces.

Keywords: Difference sequence space, BK spaces, matrix transformations, measures of noncompactness
• Maryam Ghodsi* Pages 161-184

In this article, the asymptotic distribution of the deviance statistic for some hypothesis tests concerning the parameters of the von Mises Fisher distribution is discussed. The focus is on the likelihood of the distribution which is a new exposition in the literature of the direc- tional distributions. To find the distribution of the deviance statistic, we use Chernoff’s idea about the distance from the cone built upon the null and alternative hypotheses.

Keywords: Asymptotic distribution theory, Directional data, Hypothesis testing